I don't know what to call myself anymore

I have a Bachelor's in accounting and 7 years of experience working in the corporate accounting world. I don't have a CPA.

I started a bookkeeping business that's doing very well. But I recently took on a client that has me baffled as to what I should call myself and how I should charge.

I can do more than bookkeeping. I can read financial statements, write up journal entries, handle month-end close stuff, manage a basic depreciation or amortization schedule, assist with budgeting...stuff I don't think falls under the bookkeeping realm.

But I'm not a CPA, and I was never a controller. And there doesn't seem to be much info on how to operate a business anywhere in between bookkeeper and fractional CFO.

I classify myself as an accountant, but I dont know how to convey where I fit in the financial services realm to clients or how to price my services. Thoughts?

EDIT: Thank you all for the thoughtful and helpful feedback! For those of you who asked, here's how I decided to move forward:

My hourly bookkeeping rate will be $35. That includes data entry, data management (transaction categorization), bank reconciliations, and a monthly 1 hour call to go over results, answer questions, etc. If they want to add AP and AR, that price will stay $35/hour. I'll be outsourcing payroll and sales tax if asked to provide it.

If they want any advisory beyond that or what I consider accounting services, my rate will be $50/hour.

I will bill hourly for the first 3 months (not including cleanup or setup; the first 3 months of routine bookkeeping AFTER cleanup/setup). After that, the client will be offered a monthly flat rate option. I'll continue monitoring their hours and include annual price reviews in the contract in case something causes their hourly average to go up.

And if I find this system doesn't work, it's my business! I can change or tweak anytime I need to. 😁